Many people sent me the correct answers for this puzzle. Many people correctly pointed out that depending on how you interpret the behavior of the pirates, the answer could be different, and I must confess that the directions I gave were therefore not perfect.
Here is a link to the answer to the puzzle:
http://www.educreations.com/lesson/view/solution-to-puzzle-3/4805335/?s=5du5UW&ref=link
Hope you enjoyed the puzzle, and are looking to work on the next one!
Alok Goyal's Puzzles Page 
you have the wrong solution for the 2nd version. the error happens when you considered 3 pirates.
your solution for 2 pirates is that P2 gives all 100 coins to P1 and “hope” P2 survives.
note the keyword “hope”.
if P3 gives 0 to P2, P2 would still vote for P3, to ensure his/her survival.
in general you have weak inequalities, and to make them strong, you offer them least count, i.e., 1 coin. that is, if there were epsilons then you would have given epsilon. in case of P3 offering P2, the least count, is hope to survive -> guarantee to survive. hope is open interval, and guarantee is close interval, that is it has that epsilon.
Kamal, sorry I have not had a chance to look at your comment. I will come back to you on this. In the meantime approving it in case anyone else has a comment. This was the most viewed puzzle so far đŸ™‚